Average Error: 0.1 → 0.1
Time: 14.4s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{x \cdot x + \left(-3\right)}{6}\]
\frac{x \cdot x - 3}{6}
↓
\frac{x \cdot x + \left(-3\right)}{6}
double f(double x) {
        double r62166 = x;
        double r62167 = r62166 * r62166;
        double r62168 = 3.0;
        double r62169 = r62167 - r62168;
        double r62170 = 6.0;
        double r62171 = r62169 / r62170;
        return r62171;
}
↓
double f(double x) {
        double r62172 = x;
        double r62173 = r62172 * r62172;
        double r62174 = 3.0;
        double r62175 = -r62174;
        double r62176 = r62173 + r62175;
        double r62177 = 6.0;
        double r62178 = r62176 / r62177;
        return r62178;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\frac{x \cdot x - 3}{6}\]
  2. Using strategy rm

  3. Applied sub-neg0.1

    \[\leadsto \frac{\color{blue}{x \cdot x + \left(-3\right)}}{6}\]

  4. Final simplification0.1

    \[\leadsto \frac{x \cdot x + \left(-3\right)}{6}\]

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))